A robust control approach for high-speed nanopositioning applications

Abstract

In this paper, a robust controller for the positioning of a piezoelectric tube scanner (PTS) used in an atomic force microscope (AFM) is proposed. A minimax linear quadratic Gaussian (LQG) controller is designed based on an uncertain system model which is constructed by measuring modeling error between the measured and model frequency response. This controller is robust against uncertainties introduced as a result of spillover dynamics of the scanner at frequencies higher than the first resonance frequency (900 Hz) of the scanner and the variation of plant transfer function due to temperature, humidity, and duration of operation. The proposed controller is applied to the PTS in the AFM used in the experiments to evaluate the performance of the proposed method. It is observed that the proposed scheme provides up to 12 dB closed-loop damping of the resonant mode to track the reference triangular signal. The robust performance of the proposed controller has been investigated for 0–1.96 g sample mass variation. A high positioning accuracy up to 125 Hz frequency is achieved by reducing scanner's vibration and tracking error. Higher-quality imaging up to 125 Hz scanning frequency is achieved compared to the existing PI controller and some other existing methods. This control technique may be applied to control vibration for the systems with changing frequency response due to uncertainties, such as vibration control of disc-drive system.